Question

Suppose R is the triangle with vertices (-1,0), (0,1), and (1,0). (a) As an iterated integral, ?_R (7x + 7y)² dA = ?_A^B ?_C^D (7x + 7y)² dx dy with limits of integration A = 0 B = 1 C = y-1 D = 1-y (b) Evaluate the integral in part (a). Hint: substitution may make the integral easier.

          Suppose R is the triangle with vertices (-1,0), (0,1), and (1,0).
(a) As an iterated integral, ?_R (7x + 7y)² dA = ?_A^B ?_C^D (7x + 7y)² dx dy with limits of integration
A = 0
B = 1
C = y-1
D = 1-y
(b) Evaluate the integral in part (a). Hint: substitution may make the integral easier.

Suppose R is the triangle with vertices (-1,0), (0,1), and (1,0).
(a) As an iterated integral, ?R (7x + 7y)² dA = ?A^B ?C^D (7x + 7y)² dx dy with limits of integration
A = 0
B = 1
C = y-1
D = 1-y
(b) Evaluate the integral in part (a). Hint: substitution may make the integral easier.

Added by Patricia H.

Calculus: Early Transcendentals

James Stewart 8th Edition

Instant Answer

Solved by Expert Madhur L

08/08/2023

Step 1

We can see that the triangle R is bounded by the lines y = 0, y = 1 - x, and y = 0. Therefore, the limits of integration for y are from 0 to 1 - x, and the limits of integration for x are from 0 to 1. Thus, we have: ∫∫R f(x + ty, y) dA = ∫0^1 ∫0^1-x f(x + ty, y) Show more…

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Suppose R is the triangle with vertices (-1, 0), (0,1), and (1, 0). (a) As an iterated integral, with limits of integration (b) Evaluate the integral in part (a): Hint: substitution may make the integral easier.